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Aggregation and Dispersion of Spheres Falling in Viscoelastic
Liquids

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D. D. Joseph, Y. J. Liu, M. Poletto, and J. Feng

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*J. Non-Newtonian Fluid Mech. *54, 45-86 (1994)

**Abstract **- This paper focuses on the settling of one sphere near
another or near a wall. We find maximum differences between Newtonian and
viscoelastic liquids, with repulsion between nearby bodies in the Newtonian
case and attraction in the viscoelastic case. Side-by-side arrangements of
sedimenting spheres are unstable in exactly the same way that broadside-on
settling of long bodies is unstable at subcritical speeds in a viscoelastic
fluid. The line of centers between the spheres rotates from across to along
the stream as the spheres are sucked together. The resulting chain of two
spheres is a long body which is stable when the line between centers is parallel
to the fall, but this configuration breaks up at supercritical speeds where
inertia again dominates. To explain the orientation of particles in the
subcritical case, we correlate the aggregative power of a viscoelastic fluid
with a zero shear value of the ratio of the first normal stress difference
to the shear stress and for exceptional cases we introduce the idea of the
memory of shear-thinning leading to corridors of reduced viscosity.